USAYPT 2023 Problems

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Tuning Forks The tuning fork has been used for frequency calibration since 1711, when it was invented by the great British trumpeter John Shore. For example, in the mid-1800s Leon Foucault used a tuning fork to calibrate the train whistle that drove his spinning mirror at a constant rate, allowing him to measure the speed of light to unprecedented accuracy. Unfortunately the frequency of a tuning fork can change, depending on the temperature or if it has been damaged in some way.

Explore the physics of pristine, and damaged, tuning forks. Test your hypotheses experimentally, until you have a robust model of the workings of a tuning fork that is both qualitatively and quantitatively accurate.

The Speed of Sound The speed of sound in air is a well-understood simple function of temperature, or so we are to believe. In a recent paper[1], the speed of sound travelling in pipes was measured to travel about 5% slower than in open air. Moreover, time of flight measurements of the velocity of sound have been studied in depth for centuries, and continue to this day as any literature search will reveal.

Investigate, both theoretically and experimentally, the speed of sound in air. Go into as much depth as you can, but make sure to experimentally test any theory that you present.

Investigating Optical Depth As light passes through a semi-opaque medium, it can be partially absorbed or scattered. Moreover the cross-section for absorption or scattering may be a function of the light's wavelength, producing such effects as blue skies and red sunsets. A recent paper[2] discusses simple laboratory procedures to measure the fractional absorption as a function of dye concentration and path length, however a satisfying explanation of their experimental results was beyond the scope of the paper.

Investigate, both experimentally and theoretically, the transmission of light through a semi-transparent medium. Go into as much depth as you can, but make sure to experimentally test any theory that you present.

The Electrostatic Pendulum Consider a small ball with mass m and charge q suspended on an insulative string between two large metal plates separated by a distance d with a voltage drop V between them, what is the angle of deflection? The solution to this problem is simply image.png, as one can easily show. However, in practice, this problem is more complicated than it appears, as it makes many simplistic assumptions. One recent attempt to model this more realistically[3] involves using the method of images rather than assuming a uniform electric field. Other more realistic models could involve modeling the charge distribution in the ball or the conducting plates. Alternatively, one could consider the mass and charge distribution of the insulating string, or one could consider various oscillations about equilibrium under various conditions.

Investigate, both theoretically and experimentally, the electrostatic pendulum, as well as fascinating extensions of your choosing. Go into as much depth as you can, but make sure to experimentally test any theory that you present.

[1] Sidebottom, D.L., American Journal of Physics 88, 521 (2020)
[2]Lamelas, F. and Swaminathan, S., American Journal of Physics, 88, 137 (2020)
[3] Goodman, Fischetti, and Hodges, American Journal of Physics 88, 222 (2020).